ALEX Classroom Resource

  

Using Equations to Solve Problems

  Classroom Resource Information  

Title:

 Using Equations to Solve Problems

URL:

 https://aptv.pbslearningmedia.org/resource/our20-math-7611/using-equations-to-solve-problems/

Content Source:

 PBS
Type: Audio/Video

Overview:

Students solve problems that can be represented by equations in the form p(x + q) = r and px + q = r. They start by using tape diagrams to make sense of problems (MP1) and then choose other representations to use (MP5).

Grade 7, Episode 17: Unit 6, Lesson 11 | Illustrative Math

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 7
9. Use variables to represent quantities in real-world or mathematical problems and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities.

a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality, and interpret it in the context of the problem.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Write and solve mathematical equations (or inequalities) to model real-world problems.
  • Interpret the solution to an equation in the context of a problem
  • Interpret the solution set of an inequality in the context of a problem.
  • Graph the solution to an inequality on a number line.
Teacher Vocabulary:
  • Algebraic expressions
  • Equations
  • Inequalities
  • Greater than
  • Greater than or equal to
  • less than
  • less than or equal to
Knowledge:
Students know:
  • p(x + q) = px + pq, where p and q are specific rational numbers.
  • When multiplying or dividing both sides of an inequality by a negative number, every term must change signs and the inequality symbol reversed.
  • In the graph of an inequality, the endpoint will be a closed circle indicating the number is included in the solution set (≤ or ≥) or an open circle indicating the number is not included in the solution set ( < or >).
Skills:
Students are able to:
  • use variables to represent quantities in a real-world or mathematical problem.
  • Construct equations (px + q = r and p(x + q) = r) to solve problems by reasoning about the quantities.
  • Construct simple inequalities (px + q > r or px + q < r) to solve problems by reasoning about the quantities.
  • Graph the solution set of an inequality.
Understanding:
Students understand that:
  • Real-world problems can be represented through algebraic expressions, equations, and inequalities.
  • Why the inequality symbol reverses when multiplying or dividing both sides of an inequality by a negative number.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.9.1: Define equation, inequality, and variable.
M.7.9.2: Set up equations and inequalities to represent the given situation, using correct mathematical operations and variables.
M.7.9.3: Calculate a solution or solution set by combining like terms, isolating the variable, and/or using inverse operations.
M.7.9.4: Test the found number or number set for accuracy by substitution.
M.7.9.5: Recall solving one step equations and inequalities.
M.7.9.6: Recognize properties of numbers (Distributive, Associative, Commutative).
M.7.9.7: Define equation and variable.
M.7.9.8: Set up an equation to represent the given situation, using correct mathematical operations and variables.
M.7.9.9: Calculate a solution to an equation by combining like terms, isolating the variable, and/or using inverse operations.
M.7.9.10: Test the found number for accuracy by substitution.
Example: Is 5 an accurate solution of 2(x + 5)=12?.
M.7.9.11: Identify the unknown, in a given situation, as the variable.
M.7.9.12: List given information from the problem.
M.7.9.13: Recalling one-step equations.
M.7.9.14: Explain the distributive property.
M.7.9.15: Define inequality and variable.
M.7.9.16: Set up an inequality to represent the given situation, using correct mathematical operations and variables.
M.7.9.17: Calculate a solution set to an inequality by combining like terms, isolating the variable, and/or using inverse operations.
M.7.9.18: Test the solution set for accuracy.
M.7.9.19: Identify the unknown, of a given situation, as the variable.
M.7.9.20: List information from the problem.
M.7.9.21: Recall how to graph inequalities on a number line.
M.7.9.22: Recall how to solve one step inequalities.

Prior Knowledge Skills:
  • Define inequality.
  • Define equivalent, simplify, term, distributive property, associative property of addition and multiplication, and the commutative property of addition and multiplication.
  • Define equation, solution of an equation, solution of an inequality, and inequality.
  • Compare and contrast equations and inequalities.
  • Determine if an inequality is by replacing the variable with a given number.
  • Determine if an equation is true by replacing the variable with a given number.
  • Simplify a numerical sentence to determine equivalence.
  • Recognize the symbols for =, >, <, ?, and ?.
  • Define equation and variable.
  • Set up an equation to represent the given situation, using correct mathematical operations and variables.
  • Identify the unknown, in a given situation, as the variable.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.9 Use the properties of operations to solve one-step equations and inequalities from real-world and mathematical problems.
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
18. Use variables to represent quantities in a real-world or mathematical problem and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities.

a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.
[Grade 7, 9, and linear portion of Algebra I with Probability, 11]
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Write and solve mathematical equations (or inequalities) to model real-world problems.
  • Interpret the solution to an equation in the context of a problem.
  • Interpret the solution set of an inequality in the context of a problem.
Teacher Vocabulary:
  • Algebraic expressions
  • Equations
  • Inequalities
  • Greater than
  • Greater than or equal to
  • less than
  • less than or equal to
Knowledge:
Students know:
  • p(x + q) = px + pq, where p and q are specific rational numbers.
  • When multiplying or dividing both sides of an inequality by a negative number, every term must change signs and the inequality symbol reversed.
  • In the graph of an inequality, the endpoint will be a closed circle indicating the number is included in the solution set (≤ or ≥) or an open circle indicating the number is not included in the solution set ( < or >).
Skills:
Students are able to:
  • Use variables to represent quantities in a real-world or mathematical problem.
  • Construct equations (px + q = r and p(x + q) = r) to solve problems by reasoning about the quantities.
  • Construct simple inequalities (px + q > r or px + q < r) to solve problems by reasoning about the quantities.
  • Graph the solution set of an inequality.
Understanding:
Students understand that:
  • Real-world problems can be represented through algebraic expressions, equations, and inequalities.
  • The inequality symbol reverses when multiplying or dividing both sides of an inequality by a negative number, and why.
Diverse Learning Needs:
Tags: equations, pxr, solve, tape diagram, word problems
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Comments

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Author: Kristy Lacks
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